Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s². If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

Length of each train,

$I_A=I_B=400 m$

Initial velocities of both trains, 

$u_A=u_B=72 km/h$

$=72\times \frac{5}{18}m/s \left(1 km/h=\frac{5}{18}m/s\right)$

Distance travelled by train A in 50 s

s_A = u_A ×t

(As for unaccelerated motion distance = Speed × Time)

$s_A=20\times 50=1000 m$

Distance travelled by train B in 50 s,

s_B= u_B+1/2 a_B t²

(As motion of train B is an accelerated motion)

$s_B=20\times 50+\frac{1}{2}\times 1\times {\left(50\right)}^2$

=1000 + 1250 = 2250 m

Original distance between the two trains $=s_B-s_A$

$=2250-1000=1250 m$